Phase Retrieval Via Reweighted Wirtinger Flow

Abstract: Phase retrieval(PR) problem is a kind of ill-condition inverse problem which is arising in various of applications. Based on the Wirtinger flow(WF) method, a reweighted Wirtinger flow(RWF) method is proposed to deal with PR problem. RWF finds the global optimum by solving a series of sub-PR problems with changing weights. Theoretical analyses illustrate that the RWF has a geometric convergence from a deliberate initialization when the weights are bounded by 1 and $\frac{10}{9}$. Numerical testing shows RWF has a lower sampling complexity compared with WF. As an essentially adaptive truncated Wirtinger flow(TWF) method, RWF performs better than TWF especially when the ratio between sampling number $m$ and length of signal $n$ is small.